Various Types of Five-Dimensional Warp Factor and Effective Planck Scale

TL;DR

This paper explores various five-dimensional warp factors linked through a parameter, analyzing their impact on the effective Planck scale and brane world diversity using hypergeometric functions.

Contribution

It introduces a model connecting four-dimensional and fifth-dimensional warp factors via a parameter, deriving explicit warp forms, and examining their effects on the effective Planck scale.

Findings

Warp factor forms are determined by hypergeometric functions.

Explicit warp factor forms are obtained for specific parameter values.

The model suggests extended possibilities for brane world scenarios.

Abstract

Based on the assumption that the warp factor of four-dimensional spacetime and the one of fifth dimension are tied through a parameter $\alpha$, we consider five-dimensional gravity with a 3-brane coupled to a bulk scalar field. For arbitrary value of $\alpha$, the form of the warp factor is implicitly determined by hypergeometric function. Concretely, we show that the warp factor becomes explicit form for appropriate value of $\alpha$, and study the relation between four-dimensional effective Planck scale and the brane tension. This setup allows the possibility of extending the diversity of brane world.